Question

How do you simplify and divide `(x^5-7x^3+x+1)/(x+3)`?

Answer 1

`x^4-3x^3+2x^2-6x+13` and remainder of-38

Explanation:

`color(white)(aaaaaaaaaa)` `x^4-3x^3+2x^2-6x+13`
`color(white)(aaaaaaaaaa)` `---------`
`color(white)(aaaa)x-4` `|` `x^5+0-7x^3+0+x+1`
`color(white)(aaaaaaaaaa)` `x^5+3x^4` `color(white)`
`color(white)(aaaaaaaaaaa)` `0-3x^4-7x^3`
`color(white)(aaaaaaaaaaaaa)` `-3x^4-9x^3`
`color(white)(aaaaaaaaaaaaaaaaaaaaaa)` `2x^3+0`
`color(white)(aaaaaaaaaaaaaaaaaaaaaa)` `2x^3+6x^2`
`color(white)(aaaaaaaaaaaaaaaaaaaaaaaaa)` `-6x^2+x`
`color(white)(aaaaaaaaaaaaaaaaaaaaaaaaa)` `-6x^2-12x`
`color(white)(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa)` `13x+1`
`color(white)(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa)` `13x+39`